A365056 E.g.f. satisfies A(x) = exp( x * (1+x/2)/A(x) ).
1, 1, 0, 1, -6, 46, -440, 5076, -68740, 1070056, -18835164, 369994780, -8025080096, 190501729848, -4912802070280, 136775150153656, -4088669684755440, 130620500241909376, -4441243727496127184, 160132524268963159440, -6102784264210449418144
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..403
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x*(1+x/2)))))
Formula
E.g.f.: exp( LambertW(x * (1+x/2)) ).
a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (-k+1)^(k-1) * binomial(k,n-k)/k!.